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 A173306 Triangle read by rows, generated from an array of terms in powers of triangle A173305. 2
 1, 1, 1, 1, 2, 1, 2, 2, 1, 3, 3, 1, 4, 5, 2, 5, 7, 3, 6, 10, 5, 1, 8, 14, 7, 1, 10, 19, 11, 2, 12, 26, 15, 3, 15, 35, 22, 5, 18, 46, 30, 7, 22, 60, 42, 11, 27, 78, 56, 15, 32, 10, 76, 22, 1, 38, 128, 100, 30, 1, 46, 162, 133, 42, 2, 54, 204, 173, 56, 3 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Row sums = A000041, the partition numbers. LINKS FORMULA Given triangle A173305 in which every column >0 = A000009 shifted down twice. We create an array in which n-th row = columns in (n-1)-th power of triangle A173305. Finite differences of successive columns of the array become row terms of A173306. EXAMPLE Given triangle A173305, we create an array by extracting terms in powers of A173305: 1, 1, 1, 2, 2, 3, .4, .5, .6, .8, 10, 12, 15,...; = column terms of A173305 1, 1, 2, 3, 4, 6, .9, 12, 16, 22, 29, 38, 50,...; = terms of A173305^2 1, 1, 2, 3, 5, 7, 11, 15, 21, 29, 40, 53, 72,...; = terms of A173305^3 1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 77,...; = terms of A173305^4 ... (rows quickly converge to A000041, the partition numbers). Taking finite difference terms from the top, we obtain the array: 1, 1, 1, 2, 2, 3, .4, .5, .6,..8, 10, 12, 15,...; ......1, 1, 2, 3, .5, .7, 10, 14, 19, 26, 35,...; ............1, 1, .2, .3, .5, .7, 11, 15, 22,...; ...........................1, .1, .2, .3, .5,...; ... Finally, columns of the above array become rows of A173306: 1; 1; 1, 1; 2, 1; 2, 2, 1; 3, 3, 1; 4, 5, 2; 5, 7, 3; 6, 10, 5, 1; 8, 14, 7, 1; 10, 19, 11, 2; 12, 26, 15, 3; 15, 35, 22, 5; 18, 46, 30, 7; 22, 60, 42, 11; 27, 78, 56, 15; 32, 100, 76, 22, 1; 38, 128, 100, 30, 1; 46, 162, 133, 42, 2; 54, 204, 173, 56, 3; ... CROSSREFS Cf. A000009, A000041, A173305 Sequence in context: A029283 A264404 A116482 * A276430 A325002 A182594 Adjacent sequences:  A173303 A173304 A173305 * A173307 A173308 A173309 KEYWORD nonn,tabl AUTHOR Gary W. Adamson, Feb 15 2010 STATUS approved

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Last modified March 28 07:59 EDT 2020. Contains 333079 sequences. (Running on oeis4.)